On Gaussian Divisors of Characteristic Functions
We prove the following facts: 1) For every natural number $n\geq 3$ there are $n$ characteristic functions each of which does not have a Gaussian divisor, and the products of all proper subsets of the set of these characteristic functions also does not have a Gaussian divisor, but the product of all...
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| Date: | 2024 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1088 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | We prove the following facts: 1) For every natural number $n\geq 3$ there are $n$ characteristic functions each of which does not have a Gaussian divisor, and the products of all proper subsets of the set of these characteristic functions also does not have a Gaussian divisor, but the product of all of these characteristic functions has a Gaussian divisor; 2) Every non-degenerate distribution with bounded spectrum has rudiments of a Gaussian component in the following sense: for each such distribution there is a distribution without Gaussian component, whose convolution with the original one has a Gaussian component. We also indicate a wide class of functions on the real axis, which are the ratio of two characteristic functions.
Mathematical Subject Classification 2020: 60E10, 42A38 |
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